Question 1

If d = 0.28,then we conclude that mean scores in some population have shifted 0.28 standard deviations below the mean.

Accepted Answer

The statement seems to refer to a value (d) that could be interpreted as a measure of effect size or difference, such as Cohen's d. However, Cohen's d specifically measures the difference between two means in terms of standard deviations, not a shift in the mean of a single population. Saying "mean scores in some population have shifted 0.28 standard deviations below the mean" misinterprets what such a statistic represents.

Question 2

A one-sample t test will be undefined (denominator = 0)when the same score is recorded for all participants in a study.

Accepted Answer

If all participants have the same score, then there will be no variability in the data, and the denominator of the formula for the standard error of the mean will be 0. This will result in an undefined value for the t statistic and therefore a one-sample t test cannot be performed.

Question 3

The p value is reported with the test statistic of a one-sample and a two-independent-sample t test using APA format.

Accepted Answer

The p value is an important component of reporting the results of a one-sample or two-independent-sample t test in APA format. It is typically reported alongside the test statistic, degree of freedom, and sample size.

Question 4

A two-independent-sample t test is used when the same participants are observed two times.

Accepted Answer

A two-independent-sample t-test is used when two different groups are being compared, not for comparing the same participants at two different times. A paired-sample t-test would be appropriate for that scenario.

Question 5

Effect size measures are an estimate of the size of an effect in a population.

Accepted Answer

Effect size measures provide an estimate of the magnitude of a relationship or difference between two groups or variables in a population, beyond the statistical significance of the result. Therefore, it is a measure of the practical significance of the finding, and it helps interpret the results in a broader context.

Question 6

When the difference between two groups is compared,the pooled standard deviation is used as an estimate for the population standard deviation in the effect size formula for estimated Cohen's d.

Accepted Answer

This is true. The pooled standard deviation is used in the effect size formula for estimated Cohen's d when comparing the difference between two groups.

Question 7

$\eta$² is a more conservative estimate than $\omega$².

Accepted Answer

The symbols provided do not correspond to a recognizable format or standard for expressing estimates, making it impossible to determine conservativeness based on the given sequences.

Question 8

An estimated Cohen's d is interpreted in terms of the number of standard deviations that an effect shifted in some population.

Accepted Answer

Cohen's d is a measure of effect size that indicates the standardized difference between two means. It is expressed in terms of the number of standard deviations that an effect shifted in some population. Therefore, the statement is true.

Question 9

A one-sample t test will be t = 0 when the mean difference is equal to 0.

Accepted Answer

This is true because when conducting a one-sample t test, the null hypothesis is that the population mean is equal to a specified value, which is often 0. Therefore, if the mean difference is equal to 0, then the t value will also be 0, as there is no difference to compare to the specified value.

Question 10

When scores are measured in a single group,the sample standard deviation is used as an estimate of the population standard deviation in the effect size formula for estimated Cohen's d.

Accepted Answer

The sample standard deviation is used to estimate the population standard deviation in the effect size formula for Cohen's d when scores are measured in a single group. This is because the population standard deviation is often unknown or difficult to obtain, and the sample standard deviation provides a reasonable estimate of the variability of scores within the population.

Question 11

A researcher reports that the mean difference between two groups is 20.12 and the estimated standard error for the difference is 2.83.Hence,the conclusion must be to reject the null hypothesis for a two-tailed test at a .05 level of significance.

Accepted Answer

To determine whether to reject or fail to reject the null hypothesis, we need to calculate the test statistic (i.e., the number of standard errors away from the null hypothesis mean) and compare it to the critical value. However, since the critical value is not provided in the given information, we cannot determine whether the conclusion to reject the null hypothesis is correct. Therefore, the question cannot be answered with certainty.

Question 12

A researcher computes a two-independent-sample t test and finds that the result is undefined (the denominator is equal to 0).This always happens when two groups do not differ (i.e.,the mean difference is equal to 0).

Accepted Answer

The result of a two-independent-sample t test can also be undefined when the standard deviation of one of the groups is equal to 0 or when one of the groups has only one observation. It is not always the case that the mean difference is equal to 0.

Question 13

A two-independent-sample t test is computed when mean differences are compared between two or more groups sampled from a population with an unknown variance.

Accepted Answer

A two-independent-sample t test is used for comparing mean differences between exactly two groups, not two or more groups, sampled from populations with unknown variances. For comparing means across more than two groups, an ANOVA is typically used.

Question 14

A researcher reports the following result for a lower-tail critical test at a .05 level of significance,t(40)= 1.512,and accurately concludes to reject the null hypothesis.

Accepted Answer

For a lower-tail test at a .05 level of significance, the critical t-value should be negative, and rejecting the null hypothesis would typically require the test statistic to be less than the critical value. A t-value of 1.512 suggests the test statistic is in the upper tail, not the lower.

Question 15

Measures of proportion of variance are computed the same for all t tests.

Accepted Answer

Measures of proportion of variance are computed the same for all t tests because they are all based on the same formula:$$ t = \frac{\overline{x}_1 - \overline{x}_2}{s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}} $$where:* $$\overline{x}_1$$ and $$\overline{x}_2$$ are the sample means of the two groups* $$s_p$$ is the pooled standard deviation* $$n_1$$ and $$n_2$$ are the sample sizes of the two groups

Question 16

When the proportion of variance explained by some treatment is larger than 0.25,we conclude that there is a large effect in the population.

Accepted Answer

A proportion of variance explained greater than 0.25 indicates a substantial amount of variability in the outcome measure can be attributed to the treatment or intervention, thus indicating a large effect.

Question 17

A one-sample t test will be t = 0 when the standard error is equal to 0.

Accepted Answer

The formula for calculating the standard error includes dividing by the square root of the sample size (n) which cannot be 0. Therefore, the standard error cannot be 0 and the t-statistic cannot be 0 for a one-sample t test.

Question 18

Cohen's d is a measure of proportion of variance.

Accepted Answer

Cohen's d is a measure of effect size used to indicate the standardized difference between two means.

Question 19

The critical values are reported with the test statistic of a one-sample and a two-independent-sample t test using APA format.

Accepted Answer

Critical values are not typically reported with the test statistic in APA format for t-tests. Instead, the degrees of freedom and p-value are reported, along with any necessary descriptive statistics.

Question 20

A researcher reports the following result for a two-tailed test at a .05 level of significance,t(30)= 2.020,and correctly decides to retain the null hypothesis.

Accepted Answer

The critical t-value for a two-tailed test at a .05 level of significance with 30 degrees of freedom is ±2.042. Since the calculated t-value of 2.020 is less than the critical value, we fail to reject the null hypothesis. Therefore, the researcher's decision to retain the null hypothesis is correct.

Quiz 9: Testing Means: One-Sample and Two-Independent-Sample T Tests

If d = 0.28,then we conclude that mean scores in some population have shifted 0.28 standard deviations below the mean.

A one-sample t test will be undefined (denominator = 0)when the same score is recorded for all participants in a study.

The p value is reported with the test statistic of a one-sample and a two-independent-sample t test using APA format.

A two-independent-sample t test is used when the same participants are observed two times.

Effect size measures are an estimate of the size of an effect in a population.

When the difference between two groups is compared,the pooled standard deviation is used as an estimate for the population standard deviation in the effect size formula for estimated Cohen's d.

$\eta$ ² is a more conservative estimate than $\omega$ ².

An estimated Cohen's d is interpreted in terms of the number of standard deviations that an effect shifted in some population.

A one-sample t test will be t = 0 when the mean difference is equal to 0.

When scores are measured in a single group,the sample standard deviation is used as an estimate of the population standard deviation in the effect size formula for estimated Cohen's d.

A researcher reports that the mean difference between two groups is 20.12 and the estimated standard error for the difference is 2.83.Hence,the conclusion must be to reject the null hypothesis for a two-tailed test at a .05 level of significance.

A researcher computes a two-independent-sample t test and finds that the result is undefined (the denominator is equal to 0).This always happens when two groups do not differ (i.e.,the mean difference is equal to 0).

A two-independent-sample t test is computed when mean differences are compared between two or more groups sampled from a population with an unknown variance.

A researcher reports the following result for a lower-tail critical test at a .05 level of significance,t(40)= 1.512,and accurately concludes to reject the null hypothesis.

Measures of proportion of variance are computed the same for all t tests.

When the proportion of variance explained by some treatment is larger than 0.25,we conclude that there is a large effect in the population.

A one-sample t test will be t = 0 when the standard error is equal to 0.

Cohen's d is a measure of proportion of variance.

The critical values are reported with the test statistic of a one-sample and a two-independent-sample t test using APA format.

A researcher reports the following result for a two-tailed test at a .05 level of significance,t(30)= 2.020,and correctly decides to retain the null hypothesis.

Quiz 9: Testing Means: One-Sample and Two-Independent-Sample T Tests

If d = 0.28,then we conclude that mean scores in some population have shifted 0.28 standard deviations below the mean.

A one-sample t test will be undefined (denominator = 0)when the same score is recorded for all participants in a study.

The p value is reported with the test statistic of a one-sample and a two-independent-sample t test using APA format.

A two-independent-sample t test is used when the same participants are observed two times.

Effect size measures are an estimate of the size of an effect in a population.

When the difference between two groups is compared,the pooled standard deviation is used as an estimate for the population standard deviation in the effect size formula for estimated Cohen's d.

η\etaη 2 is a more conservative estimate than ω\omegaω 2.

An estimated Cohen's d is interpreted in terms of the number of standard deviations that an effect shifted in some population.

A one-sample t test will be t = 0 when the mean difference is equal to 0.

When scores are measured in a single group,the sample standard deviation is used as an estimate of the population standard deviation in the effect size formula for estimated Cohen's d.

A researcher reports that the mean difference between two groups is 20.12 and the estimated standard error for the difference is 2.83.Hence,the conclusion must be to reject the null hypothesis for a two-tailed test at a .05 level of significance.

A researcher computes a two-independent-sample t test and finds that the result is undefined (the denominator is equal to 0).This always happens when two groups do not differ (i.e.,the mean difference is equal to 0).

A two-independent-sample t test is computed when mean differences are compared between two or more groups sampled from a population with an unknown variance.

A researcher reports the following result for a lower-tail critical test at a .05 level of significance,t(40)= 1.512,and accurately concludes to reject the null hypothesis.

Measures of proportion of variance are computed the same for all t tests.

When the proportion of variance explained by some treatment is larger than 0.25,we conclude that there is a large effect in the population.

A one-sample t test will be t = 0 when the standard error is equal to 0.

Cohen's d is a measure of proportion of variance.

The critical values are reported with the test statistic of a one-sample and a two-independent-sample t test using APA format.

A researcher reports the following result for a two-tailed test at a .05 level of significance,t(30)= 2.020,and correctly decides to retain the null hypothesis.

$\eta$ ² is a more conservative estimate than $\omega$ ².